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Traditional Graph Neural Networks (GNNs) cannot generalize to new graphs with node attributes different from the training ones, making zero-shot generalization across different node attribute domains an open challenge in graph machine learning. In this paper, we propose STAGE, which encodes *statistical dependencies* between attributes rather than individual attribute values, which may differ in test graphs. By assuming these dependencies remain invariant under changes in node attributes, STAGE achieves provable generalization guarantees for a family of domain shifts. Empirically, STAGE demonstrates strong zero-shot performance on medium-sized datasets: when trained on multiple graph datasets with different attribute spaces (varying in types and number) and evaluated on graphs with entirely new attributes, STAGE achieves a relative improvement in Hits@1 between 40% to 103% in link prediction and a 10% improvement in node classification compared to state-of-the-art baselines.